What is the Greatest Common Factor of 17574 and 17580?

Greatest common factor (GCF) of 17574 and 17580 is 6.

GCF(17574,17580) = 6

We will now calculate the prime factors of 17574 and 17580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17574 and 17580.

How to find the GCF of 17574 and 17580?

We will first find the prime factorization of 17574 and 17580. After we will calculate the factors of 17574 and 17580 and find the biggest common factor number .

Step-1: Prime Factorization of 17574

Prime factors of 17574 are 2, 3, 29, 101. Prime factorization of 17574 in exponential form is:

17574 = 2¹ × 3¹ × 29¹ × 101¹

Step-2: Prime Factorization of 17580

Prime factors of 17580 are 2, 3, 5, 293. Prime factorization of 17580 in exponential form is:

17580 = 2² × 3¹ × 5¹ × 293¹

Step-3: Factors of 17574

List of positive integer factors of 17574 that divides 17574 without a remainder.

1, 2, 3, 6, 29, 58, 87, 101, 174, 202, 303, 606, 2929, 5858, 8787

Step-4: Factors of 17580

List of positive integer factors of 17580 that divides 17574 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 293, 586, 879, 1172, 1465, 1758, 2930, 3516, 4395, 5860, 8790

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17574 and 17580. The biggest common factor number is the GCF number.
So the greatest common factor 17574 and 17580 is 6.

Also check out the Least Common Multiple of 17574 and 17580